Tim Bates, Rutgers University

Abstract

Link diagrams are combinatorial objects used to represent and study classical links in 3-space. Take your favorite 4-valent planar graph and decorate each vertex with crossing data and you get a diagram of a link. Local moves on diagrams called Reidemeister moves define an equivalence relation of link diagrams that correspond precisely to the topological notion of link equivalence. Virtual link diagrams are generalizations which geometrically may correspond to links living in other 3-manifolds apart from S^3.  In this talk we examine some properties of (virtual) knots and hopefully give some indication as to what knot theorists think counts (pun intended?) as combinatorics. 

See: https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html